Problem: Express your answer as a mixed number simplified to lowest terms. $8\dfrac{5}{13}-2\dfrac{2}{3} = {?}$
Find a common denominator for the fractions: $= {8\dfrac{15}{39}}-{2\dfrac{26}{39}}$ Convert ${8\dfrac{15}{39}}$ to ${7 + \dfrac{39}{39} + \dfrac{15}{39}}$ So the problem becomes: ${7\dfrac{54}{39}}-{2\dfrac{26}{39}}$ Separate the whole numbers from the fractional parts: $= {7} + {\dfrac{54}{39}} - {2} - {\dfrac{26}{39}}$ Bring the whole numbers together and the fractions together: $= {7} - {2} + {\dfrac{54}{39}} - {\dfrac{26}{39}}$ Subtract the whole numbers: $=5 + {\dfrac{54}{39}} - {\dfrac{26}{39}}$ Subtract the fractions: $= 5+\dfrac{28}{39}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{28}{39}$